UNIVERSITY OF LONDON University College London
Department of Electronic and Electrical Engineering
Fast Waveform Metrology:
Generation, Measurement and Application of Sub-
picosecond Electrical Pulses
Andrew JA Smith
November 1995
This thesis describes work performed at the National Physical Laboratory to improve the electrical risetime calibration of instruments such as fast sampling oscilloscopes. The majority of the work can be divided into four sections: development of an ultrafast optoelectronic pulse generator; measurement of fast electrical pulses with an electro- optic sampling system; de-embedding of transmission line and transition effects as measured at different calibration reference planes; and calibration of an oscilloscope.
The pulse generator is a photoconductive switch based on low-temperature Gallium Arsenide, which has a very fast carrier recombination time. Sub-picosecond electrical pulses are produced by illuminated a planar switch with 200 fs optical pulses from a Ti: sapphire laser system.
The pulses
are measured
using a sampling
system
with an external
electro-optic
probe in
close proximity to the switch. The electro-optic sampling system, with a temporal
resolution better than 500 fs, is used to measure
the electrical pulse shape at various
positions along the planar transmission
he. The results are compared to a pulse
propagation
model for the line. The effects of different switch geometries
are examined.
Although the pulse generator produces sub-picosecond
pulses near to the point of
generation, the pulse is shown to broaden to 7 ps after passing along a length of
transmission
line and a coplanar-coaxial
transition. For a sampling
oscilloscope
with a
coaxial input connector,
this effect is significant.
Frequency-domain
measurements
with
a network analyser,
further electro-optic
sampling
measurements,
and the transmission
line
model are combined
to find the network transfer function of the transition.
Using the pulse generator,
the electro-optic
sampling
system
and the transition knowledge,
a 50 GHz sampling
oscilloscope
is calibrated.
The determination
of the instrument
step
response
(nominal risetime 7 ps) is improved from an earlier value of 8.5 -3.5 / +2.9 ps
to a new value of 7.4 -2.1 / +1.7 ps with the calibration techniques
described.
CONTENTS
Page
ABSTRACT
...
2
CONTENTS
...
4
ILLUSTRATIVE MATERIAL
...
8
INTRODUCTION
1.1
The sampling
oscilloscope ...
12
1.1.1 History
...
12
1.1.2 Recent developments ... 12
1.2 Introduction to waveform metrology ... 14
1.2.1 Impulse response ... 14
1.2.2 Optoelectronic
approach
...
15
1.3 Organisation of thesis ... 16
1.4
Thesis
Terminology
...
17
1.4.1 Domains
and FFT ...
18
1.4.2 BSI/ IEC standards
...
18
1.4.3 Definition of oscilloscope response ... 19
1.4.4 Convolution
and deconvolution
...
21
1.5
References
to Chapter 1
...
22
2
BACKGROUND THEORY
2.1
2.2
Introduction
...
Principle of the photoconductive
switch ...
23
23
2.3 Modelling the photoconductive switch ... 242.3.1 Voltage considerations ...
24
2.3.2 Speed considerations ... 26
2.4
Photoconductive
material selection ...
28
2.5
Properties
of LT-GaAs ...
31
2.6
Wafer growth ...
33
2.7
Conclusions
...
38
2.8
References
to Chapter
2
...
39
3 DESIGN, FABRICATION AND ELECTRICAL CHARACTERISATION
3.1
Introduction
...
41
3.2 Coplanar waveguide and stripline transmission lines ... 41
3.2.1 Design equations for CPW ... 42
3.2.2 Design equations for CPS ... 45
3.3
Mask design
...
46
3.3.1 Packaging issues ... 46
3.3.2 Taper
...
48
3.3.3 Example
of devices
- design
A
...
49
3.3.4 Features
on a mask ...
50
3.4
Device fabrication
...
51
3.5
D. C. and low frequency
measurements
...
56
3.6
Conclusions
...
62
3.7
References
to Chapter
3
...
63
4 SAMPLING OSCILLOSCOPE AND ELECTRO-OPTIC SAMPLING MEASUREMENTS
4.1
Introduction
...
65
4.2
Photoconductive
switch configurations
...
65
4.2.1 CPW sliding contact
...
66
4.2.2 CPW Ruston switch ... 66 4.2.3 CPS sliding contact ...
4.2.4 Approximate response of configurations ...
67 68
4.3
Theory of EOS...
4.3.1 Pockets effect ...
4.3.2 Sampling and detection ...
69 69 71
4.4
4.5
The dye laser EOS system
The Ti: sapphire
laser EOS system ...
...
4.5.1 Prism probe
...
4.5.2 Probe station
...
73
75
75
78
4.64.7
4.5.3 Calibration of voltage ... Dye laser measurements ...
4.6.1 CRO results ... 4.6.2 EOS results ...
Ti. sapphire laser measurements ... ... ... '... 4.7.1 CRO results ...
79 79 79 84 85 85
4.8
4.9
4.7.2 EOS results
...
4.7.2.1 CPW sliding contact
...
...
4.7.2.2 CPW Auston switch ...
4.7.2.3 CPS sliding contact
...
CRO measurements
of SI-GaAs ...
EOS system limitations and response
of LT-GaAs ...
4.9.1 Noise and voltage limitations
...
4.9.1.1 Laser noise
...
4.9.1.2 EOS S/N
...
86
86
89
90
91
92
92
92
93
4.10
4.11
4.9.1.3 Dynamic range ...
4.9.1.4 Probe height sensitivity ... 4.9.2 Dye laser system resolution ...
4.9.3 Ti: sapphire laser system resolution ... 4.9.4 Temporal response of LT-GaAs ... Conclusions
... References to Chapter 4
5
DE-EMBEDDING THE TRANSMISSION LINE AND TRANSITION
5.1
Introduction
...
104
5.1.1 Approach to de-embedding
- organisation
of chapter ...
105
5.1.2 Transmission
he components
of the pulse generator
...
105
5.2 Transmission line modelling ... 107
5.2.1 Modal dispersion
ß.
...
109
5.2.2 Conductor
loss a. and conductor phase ß. ...
III
5.2.3 Dielectric loss aa ...
113
5.2.4 Radiation
loss a, . ...
114
5.2.5 Summary of terms in model ... 115
5.3 Frequency-domain measurements ... 115
5.3.1 The automatic network analyser ...
116
5.3.2 Two transition measurements
with an ANA ...
118
5.3.2.1 Alumina line
...
119
5.3.2.2 GaAs line
...
122
5.3.3 Single transition measurements with an ANA ... 124
5.3.4 Results of transmission line model in the frequency-domain ... 127 5.3.5 Comparison of model with ANA results ... 132
5.4
Time-domain
measurements
...
134
5.4.1 Two transition measurements
with a CRO ...
134
5.4.2 Results
of transmission
line model in the time-domain ... 139
5.4.2.1 Modelling of Gaussian
pulses ...
139
5.4.2.2 Summary
of Gaussian
pulses ...
143
5.4.2.3 Effect of taper
...
144
5.4.3 Comparison
of model with EOS results ...
145
5.4.3.1 GaAs line
...
145
5.4.3.2 Alumina line
...
147
5.5
The impulse
response
of a single transition ...
148
...
5.5.1 EOS measurement
of two transitions
...
148
5.5.2 Derivation of single-transition
response ...
150
5.6
...
Conclusions
152
5.7
...
.
References
to Chapter
5
153
.
...
6
THE OSCILLOSCOPE RESPONSE
6.1
Introduction
...
155
6.2
Deconvolution
...
6.2.1 Quadrature
approximation ...
155
155
6.3
6.4
6.5
6.6
6.2.2 Deconvolution
and filtering ...
6.2.3 Example
of deconvolution ...
6.2.4 Example
of uncertainties
in deconvolution
...
Jitter
...
6.3.1 Measurement
and removal of jitter ...
Deriving the oscilloscope
response ...
6.7
References
to chapter 6 ...
174
7
CONCLUDING COMMENTS AND FUTURE WORK
7.1 Introduction ... 1757.2
Concluding
comments ...
175
7.2.1 Pulse generator
...
175
7.2.2 Electro-optic sampling
...
176
7.2.3 De-embedding
...
177
7.2.4 Oscilloscope calibration ... 178
7.3 Future work and opportunities ... 178
7.3.1 Oscilloscope calibration ... 178
7.3.2 Opportunities ... 180
7.4
References
to Chapter
7
...
182
APPENDICES A Measurement of bias tees and attenuators ... 183
A. 1
Introduction
...
183
A. 2
Measurements
...
183
A. 3
Conclusions
...
184
B List of publications during project ... 185
ACKNOWLEDGEMENTS
Table 1.1
Recent
history of oscilloscope
risetimes
and NPL calibration
facilities.
Table 2.1 Some typical photoconductive semiconductors.
Figure 2.1
Simple photoconductor
circuit.
Figure 2.2 Equivalent circuit of photoconductive switch. Figure 2.3 Structure of LT-GaAs wafer.
Figure 2.4 Example of room-temperature photoluminescence of LT-GaAs- Figure 2.5 Example of X-ray analysis of LT-GaAs wafer.
Figure 2.6 X-ray analysis of SI-GaAs wafer.
Chapter 3
Table 3.1
Frequency-dependent
effect of line size and metal thickness
on impedance.
Table 3.2
Summary
of important devices.
Table 3.3
Measured
device resistances
and derived metallisation
resistivities.
Figure 3.1
Geometry
of coplanar
waveguide
(CPW).
Figure 3.2 Geometry of coplanar stripline (CPS).
Figure 3.3
Central line taper from small to large CPW.
Figure 3.4
Device A with tapers.
Figure 3.5
Example
of features
on NPL-designed
mask.
Figure 3.6 Schematic of I-V contact measurements.
Figure 3.7 I-V curve of unannealed S. I. GaAs device TL4. Figure 3.8 I-V curve of annealed S. I. GaAs device TLS.
Figure 3.9 I-V curve of unannealed LT-GaAs device PG4.
.
Chapter
Table
4.1
Laser amplitude noise.
Table 4.2
System
resolution
of dye laser and Ti: sapphire
laser EOS.
Table 4.3
Deconvolved
response
of LT-GaAs.
Figure 4.1
CPW sliding contact measurement
configuration.
Figure 4.2
CPW Auston switch measurement
configuration.
Figure 4.3
CPS sliding contact measurement
configuration.
Figure 4.4
Approximating
the capacitance
of the CPW gap by a CPS line. Dimensions
are in µm.
Figure 4.5
Schematic
of an electro-optic
modulator.
Figure 4.6
Transmission
of an electro-optic
modulator.
Figure 4.7
Dye laser electro-optic sampling
system.
Figure 4.8 Structure of LiTaO3 probe.
Figure 4.9
Ti: sapphire
EOS system.
Figure 4.10 Photograph of probing station, showing optical arms for the generation,
sampling
and CCD imaging
systems
around a device mounted
in a UTF.
Figure 4.11
Schematic
of sampling
oscilloscope
measurement
system.
Figure 4.12 Oscilloscope measurement of PG1.
Figure 4.13 Linearity of photoconductive switch with respect to bias voltage. Figure 4.14 Location of excitation points.
Figure 4.15 Oscilloscope measurement
of pulse generator at various excitation
locations.
Points 2,3, and 4 correspond
to Figure 4.13.
Figure 4.16 Dye laser EOS of PG1 with 200 pm generate-sample separation:
sampled same side of CPW as excited; sampled opposite side. Figure 4.17 Oscilloscope measurement of PG4.
Figure 4.18 EOS of CPW sliding contact with generate-sample spacing of 200 µm: sampled same CPW side as generated; sampled opposite side. Figure 4.19 EOS of CPW sliding contact with generate-sample spacing of 1.5 mm:
sampled
same
CPW side as generated;
sampled
opposite
side.
Figure 4.20 EOS of Auston switch with 200 pm generate-sample
spacing:
measurement
of top CPW slot;
measurement
of bottom slot.
Figure 4.21 Ti: sapphire
EOS measurement
of CPS sliding contact.
Figure 4.22 CRO measurement
of SI-GaAs.
Figure 4.23 Variation of EOS signal with probe height.
Figure 4.24 Background-free
autocorrelations:
measured
Ti: sapphire
trace;
x Gaussian
model; o sech2
model.
Table 5.1 Comparison of 3 mm alumina CPW S21 attenuation. Table 5.2 Comparison of 3 mm alumina CPW S21 phase.
Figure 5.1
Transmission
line components
of the photoconductive
switch.
Figure 5.2
Picture of UTF showing coax-CPW transition.
Figure 5.3
Schematic
of ANA.
Figure 5.4
Reference
planes
of two transition ANA measurements.
Figure 5.5
ANA S21
attenuation
measurement
of UTF1 and alumina
CPW.
Line lengths:
10 mm,
13 mm,
19 mm.
Figure 5.6
ANA S21
phase
measurement
of UTF1 and alumina
CPW.
Line lengths: 10 mm, 13 mm, 19 mm.
Figure 5.7 Re-plotted ANA S2, phase measurement of UTF1 and alumina CPW after
subtracting
linearities.
Line lengths:
-10
mm,
13 mm,
19 mm.
Figure 5.8 ANA S21 attenuation of GaAs lines: -- PG4, ---- TL3. Figure 5.9 ANA S21 phase of GaAs lines: - PG4, TL3.
Figure 5.10 Reference
planes
of single transition ANA measurements.
Figure 5.11 ANA S21'
attenuation
measurements
of UTF1:
de-embedded
single
transition and 5 mm CPW;
(double transition and 10 mm CPW).
Figure 5.12 ANA S21' phase measurements
of UTF1:
dc-embedded
single
transition
and 5 mm CPW;
(double transition and 10 mm CPW).
Figure 5.13 Modelled conduction loss a, for CPW lines.
Figure 5.14 Modelled dielectric loss ad for CPW lines.
Figure 5.15 Modelled radiation loss a, for CPW lines.
Figure 5.16 Modelled total attenuation factor a for CPW lines.
Figure 5.17 Modelled phase factor ß of CPW lines: small GaAs; large GaAs; alumina.
Figure 5.18 Re-plotted modelled change of phase per mm of CPW line, after
subtracting
linearities:
small GaAs;
large GaAs;
alumina.
Figure 5.19 Schematic
of photodiode
transmission
line measurement
system.
Figure 5.20 Recorded waveforms on oscilloscope: without UTF2; with UTF2 and 10 mm alumina CPW.
Figure 5.21 Recorded waveforms of GaAs circuits in UTF2: device TU (unannealed); device TL3 (annealed).
Figure 5.22 Attenuation result for UTF2 and 10 mm alumina line: deconvolved CRO; ANA.
Figure 5.23 Phase
result for UTF2 and 10 mm alumina
line:
deconvolved
CRO;
ANA.
Figure 5.24 Results of model for initial Gaussian
pulses
along GaAs CPW lines after
Figure 5.25 Figure 5.26 Figure 5.27 Figure 5.28 Figure 5.29
propagation distance: 0 mm, 1 mm, 2 mm. Results of propagation model for small GaAs CPW.
Results
of propagation
model for large GaAs CPW.
Results
of propagation
model for alumina
CPW.
Modelled effect of splitting taper into segments.
Example of EOS results showing
position
z from the generation
point:
z1 mm, FWHM=2.2ps; z=2mm, FWHM=4.8ps.
pulse evolution along GaAs line at
z= 0.3 mm, FWHM = 1.3 ps;
z= 1.5 mm, FWHM = 3.7 ps;
Figure 5.30 EOS results and propagation model along GaAs pulse generator, comprising a1 mm length of small GaAs CPW, a 0.5 mm taper and a 2 mm length of large GaAs.
Figure 5.31 EOS results and propagation model along alumina line.
Figure 5.32 EOS two-transition measurement
schematic.
Figure 5.33 Two-transition EOS waveform.
Figure 5.34 Derived single transition.
Table 6.1
Effect of filter on various parameters.
Table 6.2
Uncertainties
due to filter.
Table 6.3 Contributions to uncertainty in oscilloscope calibration. Table 6.4 Improvement in oscilloscope response.
Figure 6.1
Example of deconvolution:
effect of filter on various parameters
of the
deconvolved
result.
Figure 6.2 Example of deconvolution: filter 4 in the time-domain. FWl-1M = 9.4 ps, risetime = 5.4 ps, falltime = 5.4 ps.
Figure 6.3
Example
of deconvolution:
time-domain
results with filters 1-4.
Figure 6.4
Example
of deconvolution
in the frequency-domain:
deconvolved
result,
filter 4.
Figure 6.5 Measurement of jitter with oscilloscope histogram. Figure 6.6 SD32 impulse response. FWI M=7.7 +1.31-1.9 ps. Figure 6.7 SD32 step response. Risetime = 7.4 +1.6/-2.1 ps.
No tables or figures.
Appendix A
Table A. 1
Broadening
and bandwidth
of bias tees and attenuators.
I 1mI IR/L/Nr @ mow.
1.1 The sampling oscilloscope
1.1.1 History
In the early 1960s, a major advance was made by Hewlett-PackardI Rd 11 and Tektronix in improving the measurement of repetitive time-domain pulses and transients by the development of the sampling oscilloscope. This provided short duration time measurements by a method known as equivalent time sampling, where a single sample from a successive repetition of a train of similar pulses is captured on an instrument display, with the next sample being acquired and displayed at a slightly different time relative to the starting pulse, so building up a picture or waveform of the pulses in the time-domain. The advantage of such an instrument readily became apparent - the measurement time to acquire and display a waveform was decoupled from the actual duration of the pulses (for example, a train of nanosecond pulses could be acquired over milliseconds, the time corresponding to multiples of the pulse repetition frequency) - and the temporal resolution limit of the real-time cathode-ray oscilloscope was surpassed.
1.1.2 Recent developments
Sampling oscilloscopes
and electrical pulse generators
are now commercially
available
with bandwidths
greater than 50 GHz or risetimes
less than 7 ps. The drive behind the
development
of such
high-bandwidth
systems
has been rapid advances
made in the fields
of optoelectronics,
computing
and telecommunications.
Traceability
of such systems
to
national
standards
is important,
supporting
market sectors
whose emerging
technologies
rely on such systems
and encouraging
growth by the provision of a sound metrological
base.
Research
to provide electrical risetime measurements
traceable
to national standards
has
been active at the National Physical Laboratory (NPL) in the United Kingdom, the
National
Institute for Standards
and Technology
(NIST) - formerly the National Bureau
I nm wucnuN
of Standards
(NBS) - in the United States and other world class standards
laboratories.
It is worth emphasizing
that the provision of a facility to calibrate sampling
oscilloscopes
and pulse
generators
to specification
is not a trivial problem.
If a 50 GHz oscilloscope
has
a specified
risetime
of less than 7 ps, then in theory one requires
a risetime
measurement
capability
of 5±2 ps, 611 ps or 6.5 ± 0.5 ps etc.
Table 1.1 shows some of the oscilloscopes
available
in recent years and contrasts their
risetimes
with the level of calibration
NPL has been able to attain since starting a service
in 1988. The author of this thesis has been closely involved with the research work at
NPL since 1989. This text outlines the applied research which culminated in the improved 1994 facility, with NPL close to being able to calibrate a 50 GHz oscilloscope to specification.
Table 1.1 Recent history of oscilloscope risetimes and NPL calibration facilities.
Example
of
Typical Risetime
NPL Calibration facility
Oscilloscope
/ ps
year
response
/s
Tektronix S4
HP 1430A
<28
1988
25 t4
HP 54120
Tektronix SD26
<16
1990
18 f 3.5
HP 54121
Tektronix SD32
<7
1992
10: L2
1994
8±2
I INTROWCRON
1.2
Introduction to waveform metrology
A waveform - defined fully in the thesis terminology - is a measured pulse or transient. Metrology is the science of measurement. The core theme of this text is waveform metrology, where measurements are described, typically shorter than 20 ps, of pulses or transients associated with the development of standards to calibrate sampling oscilloscopes.
1.2.1 Impulse response
The performance of an oscilloscope is usually described by its response to one of two mathematical concepts: an electrical impulse, with infinitesimal short pulse duration; 21 or a Heaviside step, with infinitesimal short risetime. l'l
In theory, if an infinitesimal short pulse generator were available and connected
to an
"ideal" oscilloscope
- with perfect lossless
and distortion-free connectors
- then the
oscilloscope
would display such a function. A real oscilloscope
would, however, not
reproduce
the function perfectly, due to the inherent limitations of the oscilloscope
(and
indeed
any measuring
instr unent). The impulse
response
of the oscilloscope
describes
the
extent to which the instrument does not behave in an idealized manner. In this
hypothetical
case,
the oscilloscope
measurement
of the infinitesimal
pulse would define
the impulse
response
of the instrument.
In practice,
a pulse
generator
capable
of producing
an infinitesimal
pulse is not required.
As long as the pulse generator has a duration significantly shorter than the nominal
response
time of the oscilloscope,
then accurate characterisation
of the oscilloscope
is
possible.
However,
the technology
to make state-of-the-art
electrical
pulse generators
has
often been similar to that used to make state-of-the-art
oscilloscopes.
One example of
such a pair of instruments,
still much in use today, is the Tektronix S4 sampler
and S52
pulse generator. Throughout most of the history of the sampling oscilloscope,
the
temporal resolution of the best commercial electrical pulse generators has not been
I UrrawuCnci
significantly faster than the response
of oscilloscopes
of the same era. The current
situation is very similar. Although convolution techniques (addressed
later) can
compensate
to a certain extent, alternative
methods
are needed
to enable
the accurate
characterisation
of sampling
oscilloscopes
to provide traceability.
1.2.2 Optoelectronic approach
The pulsed electrical measurement system developed at the NPL uses a picosecond optoelectronic technique to generate electrical pulses that are faster than can be generated by purely electrical means. The fast electrical pulses are generated by illuminating photodiodes or photoconductive switches with femtosecond lasers. The resultant waveform recorded on an oscilloscope (CRO) is the convolution of the oscilloscope impulse response with the pulse generator signal, together with the response of the interconnecting transmission lines. The pulse generator signal is measured, independently of the CRO, using electro-optic or photoconductive sampling techniques with sub- picosecond resolution. The oscilloscope response is obtained by deconvolution of the test
signal from the recorded waveform, normally performed with associated windowing and filtering techniques.
The pulse generator used in the calibration system at the outset of this project was a
commercially
available
50 GHz Schottky
barrier photodiode,
1'l capable of producing 9 ps
pulses. Using such a system, the NPL established
facilities to calibrate sampling
oscilloscopes
and electrical pulse generators
with risetimes
down to below 10 ps or
bandwidths
of 35 GHz and above.
1'] To improve the temporal resolution of the system
and to reduce
the uncertainties
in the existing measurements,
a faster pulse generator
was
required.
It was to meet this, and other requirements,
that the pulse generator
project at
the NPL was initiated, on which some of this thesis is based.
To achieve the stated aim, various options were considered, such as advanced
photodiodes
and non-linear
transmission
lines.
l'1 However, the photoconductive
switch
appeared
to offer the simplest and most cost-effective
route to achieve
the target. This
I n«RODUCCION
switch
works on the principle
of changes
in the conductance
of a material,
induced
by the
injection
of a large number
(>1017
cm 3) of electron-hole
pairs. If the electron-hole
pairs
are produced by illumination with photons from a femtosecond
laser, and the carrier
characteristics
of the material are fast, then rapid changes
in the conductance
of the
material may be produced
which provide a mechanism
for a fast pulse generator.
1.3 Organisation of thesis
This introductory chapter concludes
in section 1.4 by introducing and defining some of
the terminology used in this thesis. The content and organisation of the rest of the thesis follows below.
The principle of the photoconductive
switch is investigated
in section 2.2 and a simple
model developed
(section 2.3). The relative merits of semiconductor
photoconductive
materials are discussed
in section 2.4 and the growth and properties of the favoured
material for waveform metrology, low-temperature
GaAs, are described
in sections 2.5
and 2.6 respectively.
Chapter 3
In section 3.2, design equations for coplanar transmission lines are discussed and photoconductive devices using such lines are designed (section 3.3) and fabricated
(section 3.4). The devices
are electrically
characterised
in section 3.5.
Photoconductive
switch measurement
configurations
are described
in section 4.2. The
theory of electro-optic sampling
(EOS) is summarised
in section 4.3, and EOS systems
with a dye laser (section 4.4) and a Ti: sapphire laser (section 4.5) are described.
Measurements
made with a sampling
oscilloscope
and the EOS systems
are explored
in
section 4.6 (dye laser) and section 4.7 (Ti: sapphire laser). The chapter concludes
by
I IM'RWUC ON
describing
the EOS system
limitations and deriving the response
of the photoconductor
(section 4.9).
Section S. 1 introduces the concept of de-embedding. A transmission line model is developed in section 5.2. In section 5.3, frequency-domain measurements of planar lines and transitions are performed with a network analyser, and the results compared with the model. Time-domain measurements of planar lines and transitions are also made with a sampling oscilloscope and the EOS system, and the results compared to the model (section 5.4). Using a two-transition measurement scheme and previous results in the chapter, the impulse response of a transition is derived and uncertainties are calculated (section 5.5).
Chapter 6
In section 6.2, a deconvolution technique and the uncertainties
associated
with it are
described
with the aid of an example.
The measurement
of jitter is described
in section
6.3, again with the aid of an example. Using the previous sections and the results of
chapter
4 and chapter 5, the response
of a sampling
oscilloscope
is determined
(section
6.4). The uncertainties
in the impulse and step response
are calculated
in section 6. S.
Chapter 7
The thesis concludes
with closing comments
and suggested
future work
Appendix A
Some results and remarks on the measurement
of bias tees and attenuators are
summarised.
1.4 Thesis Terminology
A key issue
in metrology is precision.
Because
of this, there is a need to be specific about
I n4 RcWCfl 4
definitions
and terminology.
1.4.1 Domains and FFT
This thesis uses the two domains most applicable in describing the electrical and
optoelectronics
work associated
with the calibration
of sampling
oscilloscopes,
namely
the time and frequency-domains.
Time-varying
changes
in electrical voltages are represented
by the electrical waveform
V(t). The frequency
spectrum, S(w), of the time-domain
waveform is defined as its
Fourier transformm21:
40
S(o) .f V(t) eýý''` s (1.1)
40
and conversely,
V(t) is defined
as the Fourier transform of S((j):
40
V(t)
.
2ir
fS() eM do
, (1.2)
where co is the frequency
in radians.
In practice, measurements
consist of discrete
numbers
of points defined within limited
ranges. Therefore,
discrete
transforms,
such as the Fast Fourier Transform (FFT), are
used to approximate the above integrals.
1.4.2 BSI/ IEC standards
Further details of some of the following terms and definitions are found in the relevant
standards
publications.
11
A wave is a modification of the physical state of a medium which propagates in that
medium as a function of time as a result of one or more disturbances.
Pulses and
I IMRwuCfON
transitions are included in the wave definition. A waveform is a manifestation,
representation
or visualization of a wave, pulse or transition. Put succinctly - the
measurement
process
yields a waveform from a (physical)
pulse.
A single pulse waveform (i. e. one that departs from, and then returns to, a nominal state) has a large number of terms associated with it. The pulse start time is defined as the instant specified by a magnitude referenced point, usually the mesial or 50 per cent point of the first transition. The pulse stop time is similarly defined for the last transition. The pulse duration is the duration between the pulse start and stop times. An alternative term for the pulse duration, used in this text, is the Full-Width-at"Half"Maximum (FWHM).
The proximal and distal points are usually specified to be at the 10 and 90 per cent reference magnitudes respectively. The first transition duration is the duration between the first proximal and distal points of the pulse transition. This thesis uses previous BSI
notation, and defines the "risetime" to be the first transition duration, as defined above, and the "falltime" to be the last transition duration
It should be noted that for comparison
purposes
it is occasionally
useful to quote the
proximal
and distal points defined
at 20 and 80 per cent respectively,
giving an alternative
transition duration. These
are clearly referred to as the 20%-80% risetime or falltime.
1.4.3 Definition of oscilloscope response
The expression
"measurement
of the response
of an oscilloscope"
is imprecisely
defined
and can include many possibilities.
Descriptions
such as "a 50 GHz oscilloscope"
are
frequently
used.
Whilst not incorrect, the use of single parameter
definitions
in either the
time or frequency-domains
can be misleading,
and may not be helpful to the user. Such
terminology can also encourage
manufacturers
to raise the published bandwidth. For
example, higher frequency components
can be tweaked to the detriment of lower
frequencies,
providing
an instrument
whose
time-domain
performance
is less well-behaved
than before the tweaking. National standards
laboratories
encourage
good practice by
I INiRwUCIlON
providing waveforms
which describe
more fully the performance
or response
of the
sampling oscilloscope than can be provided by parametric definitions. However,
parametric
definitions
can still be useful, providing the above is taken into account.
The risetime of an oscilloscope
is the single parameter
quoted by many to describe
the
step response
of an oscilloscope
to an Heaviside
step functioni'l input. The step response
is the integral of the impulse response,
as previously
defined.
For a Gaussian
impulse
response,
duration Tom, it can be shown °l that
-"1.089 (1.3)
TPWMI
where Z,, is the risetime (of the step response).
The bandwidth,
or -3 dB frequency,
of the oscilloscope
is defined
to be the frequency
at
which the power spectrum
decreases
by a factor of two from the d. c. value. The power
bandwidth should not be confused with the frequency at which the voltage drops by a
factor of two (sometimes
loosely referred to as the voltage bandwidth); the frequency
at
the -3 dB power point is equivalent to the frequency at the -6 dB voltage point.
For a Gaussian
impulse
response,
0.34 0.31
sK t
IPWMW
(1.4)
where
fo is the (power) bandwidth.
It is worth noting that such a relation depends
on the
shape of the response. Although a practical oscilloscope response often has a similar shape to a Gaussian, an exponential decay (RC time constant) is frequently assumed. For
an exponential
decay,
0.35
(1.5)
I INMOVUCf ON
where Tt is the risetime of the integrated
decay.
1.4.4 Convolution and deconvolution
Convolution is best described here in the context - fast waveform metrology - in which it is to be used. When an instrument such as a sampling oscilloscope is used to measure a time-domain pulse or transient, the recorded waveform, h(t), is not a true representation of the original pulse, at), but is affected by the non-perfect oscilloscope, represented by the system response. The signal fit) is convolved with the oscilloscope system response g(t), to provide the measured waveform h(t) recorded on the oscilloscope - see equation (1.6); x is a dummy variable. Convolution is ubiquitous in measurement as all measuring instruments have a finite system response or resolving limitation.
ob
h (t) " ff(x) g (t-x) dc (1.6)
The symbol 0 is used to represent
a convolution,
such that equation
(1.7) is equivalent
to equation (1.6):
h (ý) - f(t) 0g (t)
(t. 7)Deconvolution
is the inverse of convolution. Deconvolution is required to recover the
desired
signal
from an instrument-limited
measurement
process.
In the example,
a known
oscilloscope
system
response
may be deconvolved
from the recorded data waveform to
obtain
the original signal. The result of jitter, noise and filtering on practical examples
of
deconvolution
is addressed
in chapter 6.
It is worth noting that in chapter 6 the application is reversed - the oscilloscope
system
response
is the desired
quantity,
which is found by deconvolving
a known pulse generator
signal from the recorded
data waveform
I INiRODUC110N
1.5 References to Chapter 1
1
Hewlett Packard
Co, "Time Domain Reflectometry",
Application Note 62, Palo
Alto, CA, USA, 1964.
2
R.
N. Bracewell,
"The Fourier
Transform
and Its Applications",
McGraw-Hill Inc,
1986.
3 P. E. Stuchert, "Pulse Standards: Basic Tools for Waveform Analysis", IEEE Trans. Instr. Meas. IM-31,1982, pp 192-198.
4
D. G. Parker, "Indium Tin oxide/GaAs Photodetectors for M llimetric-wave
Applications",
Electr. Lett., Vol. 22,1986, pp 1266-1267.
5 D. Henderson, A. G. Roddie and A. J. A. Smith, "Recent Developments in the Calibration of Fast Sampling Oscilloscopes", IEE Proc. A, VoL JA No. 5, Sept
1992, pp 254-260.
6 M. J. Rodwell and M. Kamegana, "GaAs Nonlinear Transmission Lines for
Picosecond
Pulse Generation
and Millimetre Wave Sampling", IEEE Trans.
4, No. 7, July 1991, pp 1194-1204.
7
British Standard guide to "Pulse Techniques
and Apparatus", BS-5698 BSI,
London, 1989 (identical to IEC 469.1).
8
D. Henderson, "Measurement
of the Temporal Response
of a Picosecond
Oscilloscope
by Optoelectronic
Techniques",
Ph.
D. Thesis,
University College
London, July 1989.
2 13ACKGROUND THEORY
2.1 Introduction
This chapter provides some theoretical and experimental background to the photoconductive switch. The principle of the photoconductive switch is first summarised and the principle further explored by the development of a simple model. Criteria to select a suitable photoconductive material - from which a pulse generator for metrology can be fabricated
- are explored, and after considering the criteria a semiconductor material, low- temperature (LT) GaAs, is chosen. The published properties of the material are summarised. Finally, the growth of LT-GaAs is described.
2.2 Principle of the photoconductive switch
A photodetector or optoelectronic converter is defined here to be a rectifying device
which converts
a.
c. light to d. c. current. Photodiodes
and photoconductors
are classes
of
photodetector. A photodiode consists of a semiconductor
junction (p-n, p-i-n, etc. )
operating under reverse bias. Details are provided in a wide range of literature.
UJ
A
photoconductor
usually consists
of two contacts separated
by a semiconductor
region
(Figure
2.1). Optical illumination of the semiconductor
material
results in the generation
of electron-hole
pairs, which increases
the conductivity of the material.
The conductivity o is given by:
Q"9(pen"NtP) . (2. l)
where n and p are the number densities of free electrons and holes, P. and µp their
respective
mobilities,
and q the electronic
charge.
A voltage source connected
across
the
two contacts drives a current through a load resistor. Changes
in optical illumination
produce
changes
in the conductivity of the semiconductor,
and thus change
the electrical
current generated
in the load. The optical illumination for ultrafast photoconductive
2 BACKGROUND 1 HEUK r
switches is usually provided by a laser, as an intense source with ultrafast changes in
illumination is required.
V
load
resistor
Figure 2.1 Simple photoconductor circuit.
A pulse generator suitable as a calibration source may have two alternative output shapes:
a pulse, starting and returning to zero amplitude; or a step, consisting of a rising edge
followed by a flat top. In practice, the output of a photoconductive step generator displays
a slow exponential decay in signal after the initial step. The application of step generators
to oscilloscope calibration has previously been addressed121 and this thesis concentrates on
developing a photoconductive impulse generator.
2.3 Modelling the photoconductive switch
2.3.1 Voltage considerations
A model for the voltage produced by a photoconductive switch can initially be obtained using a quasi-stationary treatment. The photons illuminating the semiconductor are all assumed to absorb uniformly within the thickness of the semiconductor active layer, except for the photons which are reflected.
24
2 DACKGROU D TI WOR?
Illumination of the semiconductor
with a modeloeked
laser generates
N` free carriers
(electron-hole
pairs) per optical pulse:
Ns - rý " f p'" hu . (1-R)"(1-. "4) (2.2)
where q is the quantum efficiency for production of free carriers, P,,, is the average optical power, f, is the repetition frequency of the laser, by is the energy of one photon, R is the optical reflectivity, a. is the optical absorption coefficient, and d the thickness of the semiconductor layer. The generated carrier density ng is determined from
nN t (2.3)
ldw
where 1 is the gap separation and w is the gap width.
For example, assuming r=1, an illumination of 5 mW at 800 nm and 80 MHz onto a
2 pm thick GaAs layer produces a value of N. = 1.5 x 108. If the optical beam diameter
is 20 pm then ng = 2.4 x 10" cm 3. This is quite a significant value, larger than typical
doping levels, and so may be expected
to alter the properties
of the material.
The photo-induced change in conductivity in the semiconductor can be estimated by substituting equation (2.3) into equation (2.1), assuming µb « µQ and N=P for excitation levels greater than the intrinsic doping. The resistance across the switch, ý, is calculated from the conductivity:
R 1. ý2
.
1. jo dw
qµß tý
hu
(2.4)
In the example, the above terms are known except the electron mobility µa A simple
equivalent circuit of the photoconductive
switch is shown in Figure 2.2. Zo is the
impedance
of the transmission
line before and after the switch, F., is the total metal-
semiconductor
contact
resistance
in the circuit, Ra(t) is the gap or switch resistance
(which
will later be described
as a function of time), and C. is the capacitance
of the gap. The
2 BACKGROUND 71 CORY
circuit acts as a potential divider such that the switched
voltage V(t) is given by
Z V(r) . tip` "
2Z@. R. R, (1)
where Vb is the d. c. bias
voltage.
If it is assumed that a switching efficiency of 5% of the bias voltage enables accurate sampling oscilloscope
Zo
Rg(t)
vb I
cý
(2ä)
Zo
Figure 2.2 Equivalent circuit of photoconductive switch.
Rc
V(t)
and electro-optic
sampling analysis (e. g. a 10 V bias produces a 20 mV photoconductively-generated peak), then for typical 50 A geometry, R, and RQ(t) must together be lower than approximately
900 Q. Usually F, « Ra(t). To achieve such a gap resistance, a minimum intensity of
optical illumination
and gap length 1 are defined,
given the material's
mobility.
The above quasi-stationary treatment enables a change of switch resistance from a known number of incident photons to be estimated in the static case. The photoconductive switch is to be used to generate ultrafast electrical pulses from ultrafast optical pulses provided by the laser. Therefore, the factors which affect the speed of performance must also be discussed.
2.3.2 Speed considerations
The bulk photoconductor shown in the previous section (Figure 2.1) is ideal for low- speed, high-power applications. However, if ultrafast changes in photoconductivity are to be used to produce fast electrical pulses then an alternative faster geometry is required,
such as the coplanar transmission lines introduced and described in chapter 3. Coplanar photoconductive devices can be fabricated from semiconductor substrates or substrates
2 aAQCCRWND n ffCRY
with appropriate
active semiconductor
layers,
usually on the substrate
top. Suitable
fast
semiconductor materials are discussed in section 2.4.
The coplanar photoconductive switch consists a pattern of metallisation deposited on the top of the semiconductor. Various geometries are possible, including the coplanar waveguide sliding contact, coplanar waveguide series-gap, and the coplanar striplinc sliding contact, referenced, discussed and measured in chapter 4. All the devices used in this thesis assume complete optical illumination across the gap in the metallisation defined
on the semiconductor. Alternative photoconductive mechanisms such as the non-uniform illumination or covered-gap technique'31, where fast pulses are obtained from a partially- illuminated gap across a slow semiconductor, are not further discussed here.
Two properties which affect the temporal response of a photoconductor are the dielectric relaxation time and the free carrier lifetime. Given an infinitely short optical excitation, electron-hole pairs in the semiconductor are generated extremely quickly, in the short time
it takes for particles to separate physically. The field distribution, and hence conductivity, do not simultaneously change since initially the space charge of the electrons and holes are neutralised. Drift in opposite directions to the applied field creates a space charge field. The dielectric relaxation time, rd, is defined as the time taken for the space charge dependent field in the photoconductor to evolve and is a complicated function of the semiconductor, geometry and illumination. t1
The photo-generated carriers recombine at a rate given by the free carrier lifetime, z&, causing a corresponding decrease in photoconductivity. The free carrier lifetime of a semiconductor depends on the semiconductor and the recombination mechanism. For example, impurities can act as recombination centres by trapping free carriers and shortening the lifetime. The decay time depends on the type and cross-section of the impurity, but the decay is non-radiative. Such a recombination is frequently used when ultrafast photoconductive switches are required.
Two further recombination
mechanisms
are summarised
below, but are not as important
2 1ACKGROUND 11 ECRY
for the operation of an ultrafast photoconductor. Radiative recombination, or luminescence, involves the excess energy being given up by emitting photons. Such a process is relatively slow, often in the order of tens of nanosecond. )51 Another non- radiative (but slow) carrier decay mechanism is three-particle Auger recombination. The excess energy raises other free carriers to higher states in their bands which subsequently relax by the emission of phonons. 15'
Other factors which affect the temporal response of the photoconductor include the
parasitics
associated
with the switch geometry
(estimated
in chapter 4) and the ability of
the transmission
line to propagate fast pulses (estimated
in chapter 5).
Returning to equations (2.4) and (2.5), the quasi-stationary approximation to the switched voltage can be extended to apply to the fast photoconductor. The switch resistance was calculated from the energy of one optical pulse. As a first approximation, this resistance can be multiplied by the ratio of the optical pulse duration to the free carrier lifetime, providing a value for the average switch resistance over the duration the switch is "closed". an effect this adds tifr to the denominator of equation (2.4) and replaces P,,, and f with the peak power of the optical pulse. )
A useful figure of merit for photoconductors
is the lifetime-mobility product, 1s' which
describes
the sensitivity
of the photoconductor
to photoexcitation.
In the above paragraph,
the estimated
switch resistance
is inversely
proportional to this product.
In summary, the risetime of a pulse generated by a photoconductor depends mainly on the
rising edge
of the optical excitation
and td, and the falltime depends
mainly on the falling
edge of the optical pulse and zf,.
2.4 Photoconductive material selection
The following properties are important in the selection of a semiconductor material
2 DACKGROUNU III MY
suitable for use in a metrological
photoconductive
switch: band-gap;
wavelength;
free
carrier lifetime; mobility, responsivity, contacting and ageing.
The band-gap, E., of a semiconductor
is the energy separating the bottom of the
conduction band and top of the valence band. The optically-induced
generation
of
electron-hole pairs in an intrinsic semiconductor
requires incident photons to have
sufficient energy to transfer an electron or hole between the two bands. The availability
of a laser with suitable
wavelength
is therefore an important consideration
in the design
Table 2.1 Some typical photoconductive semiconductors.
Band-gap Equivalent Free Carrier Estimated Semiconductor Es Wavelength Lifetime ti f, Mobility
e A Mn s em2Ns
Cr-doped
1.42
870
50 - 200
1000
GaAs
MBE LT-
1.42
870
<1
200
GaAs
Amorphous
1.12
1110
1-10
1
Si
Ion-damaged
1.12
1110
<1
20
SOS
MOVPE 1.56 800 <1 150
CdTe
of photoconductive
switches. Table 2.1 shows examples of some semiconductors
previously
utilised for fast photoconductive
switches
along with various properties.
The
equivalent wavelength
defines the cut-off wavelength above which the photons have
insufficient energy for absorption in the semiconductor. Below the wavelength, the
number
of photons absorbed
is estimated
in the previous section.
2 nA(XCRCUND 11 JEORY
Many materials, included those in Table 2.1, have sub-picosecond dielectric relaxation times. However, specialised semiconductor growth techniques are needed to achieve sub- picosecond recombination lifetimes, r f, Such techniques introduce recombination centres
or traps into the semiconductor by various methods, including: doping (Cr-doped GaAs); '61 the use of grain boundary defects (amorphous Si); t71 ion-implantation damage (silicon-on sapphire); '81 epitaxial growth (CdTe); ' 1 or by low-temperature epitaxial growth (LT-GaAs). Properties of LT-GaAs are described in section 2.5.
In addition to time-resolved carrier dynamics, the responsivity of a photoconductive device is an important consideration. The pulse amplitude needs to be sufficient to provide adequate signal-to-noise in the metrological application. Factors which affect the responsivity include the semiconductor mobility, resistivity, and contact resistance, as
shown in the previous section.
Mobility is an important
consideration
for charge transport because
it describes
the effect
an applied
electric
field has on the motion of an electron or hole. A material with a higher
mobility will, given similar device conditions, produce pulses of larger amplitude. An
unfortunate consequence
of the introduction of traps/recombination
centres in many
materials
is the subsequent
decrease
in mobility. Materials which maintain a relatively high
mobility and short free carrier lifetime are therefore ideal.
The interface, or contact between a semiconductor and metal has been the subject of much research. '101 The ohmic contact can be defined as a contact with a linear I-V characteristic, that is stable in time and temperature, and contributes as little parasitic resistance as possible. This ideal contact is not always possible to fabricate. Placing a metal on a wide band-gap semiconductor, such as GaAs, depletes a region of the semiconductor (beneath the metal) of carriers, producing a rectifying junction known as a blocking or Schottky contact. The I-V characteristic of such a junction is non-linear, as the applied voltage can alter the depth of the depletion region.
Most semiconductor
devices
require
an ohmic contact for effective operation unless non-
2 UAaCGROUND 11 M MY
ohmic behaviour
is particularly advantageous.
For a photoconductive
device which is
transit-time-limited
- i. e. when the free carrier lifetime is much longer than the time of
travel between
the two contacts or electrodes
- then ohmic contacts
will decrease
the
series
resistance,
R,,, of the device, and in the external circuit produce higher-amplitude
pulses.
For devices in this thesis, where the free carrier lifetime is shorter than the transit-time, some carriers will reach one electrode and must be replaced by carrier injection from the other electrode. An ohmic contact is more efficient at carrier replacementts1 and therefore
increases the device responsivity, although careful consideration is required further to define the relative merits of the ohmic contact. This is not further discussed here.
One further property to consider is ageing. It has been found with some silicon-on- sapphire devices that ion-induced damage can vary significantly over time-periods of months. There is no evidence to suggest LT-GaAs suffers similar ageing problems. In addition to this, some contact metallurgies have been found to be unstable over similar time scales. Clearly such factors require consideration in choosing a suitable photoconductor for metrological application.
Considering
all the above
factors,
and referring back to Table 2.1, it was decided
to grow
LT-GaAs as a photoconductive
material, due to its published
fast carrier recombination
time, relatively high mobility and expected
long-term performance
stability in a switch.
2.5
Properties of LT-GaAs
MBE growth of GaAs is usually performed at a substrate
temperature
of around 600 °C.
It has been found, however, that GaAs grown at lower temperatures (LT-GaAs) has some useful properties. LT GaAs was first grown as a buffer layer to eliminate side-gating and back-gating effects in GaAs MESFET devices, taking advantage of the high resistivity of the annealed material. 1111 When initially used as the photoconductive material in a
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